Simplify the following expression and state the condition under which the simplification is valid: $r = \dfrac{t^2 - t}{t^2 - 11t + 10}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{t^2 - t}{t^2 - 11t + 10} = \dfrac{(t)(t - 1)}{(t - 10)(t - 1)} $ Notice that the term $(t - 1)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(t - 1)$ gives: $r = \dfrac{t}{t - 10}$ Since we divided by $(t - 1)$, $t \neq 1$. $r = \dfrac{t}{t - 10}; \space t \neq 1$